(2024) 22:297
Chaturvedi et al. BMC Medicine
https://doi.org/10.1186/s12916-024-03515-8

BMC Medicine

RESEARCH ARTICLE

Open Access

Estimating the relative importanceof epidemiological and behavioural parameters
for epidemic mpox transmission: a modelling
study
Madhav Chaturvedi1, Isti Rodiah2, Mirjam Kretzschmar3, Stefan Scholz4, Berit Lange2,5, André Karch1† andVeronika K. Jaeger1*†   Abstract
Background Many European countries experienced outbreaks of mpox in 2022, and there was an mpox outbreakin 2023 in the Democratic Republic of Congo. There were many apparent differences between these outbreaks
and previous outbreaks of mpox; the recent outbreaks were observed in men who have sex with men after sexual
encounters at common events, whereas earlier outbreaks were observed in a wider population with no identifiablelink to sexual contacts. These apparent differences meant that data from previous outbreaks could not reliably be
used to parametrise infectious disease models during the 2022 and 2023 mpox outbreaks, and modelling efforts were
hampered by uncertainty around key transmission and immunity parameters.
Methods We developed a stochastic, discrete-time metapopulation model for mpox that allowed for sexualand non-sexual transmission and the implementation of non-pharmaceutical interventions, specifically contact
tracing and pre- and post-exposure vaccinations. We calibrated the model to case data from Berlin and used Sobol
sensitivity analysis to identify parameters that mpox transmission is especially sensitive to. We also briefly analysed
the sensitivity of the effectiveness of non-pharmaceutical interventions to various efficacy parameters.
Results We found that variance in the transmission probabilities due to both sexual and non-sexual transmission had
a large effect on mpox transmission in the model, as did the level of immunity to mpox conferred by a previous smallpox vaccination. Furthermore, variance in the number of pre-exposure vaccinations offered was the dominant contributor to variance in mpox dynamics in men who have sex with men. If pre-exposure vaccinations were not available, both the accuracy and timeliness of contact tracing had a large impact on mpox transmission in the model.
Conclusions Our results are valuable for guiding epidemiological studies for parameter ascertainment and identifying key factors for success of non-pharmaceutical interventions.
Keywords Infectious disease modelling, Mpox, Global sensitivity analysis†

André Karch and Veronika K. Jaeger contributed equally as last authors.

*Correspondence:
Veronika K. Jaeger
veronika.jaeger@ukmuenster.de
Full list of author information is available at the end of the article© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Chaturvedi et al. BMC Medicine(2024) 22:297

BackgroundMpox, formerly known as monkeypox [1], is a zoonosis
caused by an orthopoxvirus which results in a smallpoxlike disease in humans. Mpox was first discovered inhumans in 1970 in Central and Western Africa [2]. Later,
infections were also observed on other continents—thelargest outbreak hitherto occurred in the United States in
2003, where 47 confirmed and probable cases were identified, all having contracted the disease from animals [3].
Other infections in non-endemic regions have occurredsince then, usually associated with travel [4–6]. There isevidence to show that smallpox vaccination grants somelevel of immunity against the mpox virus [7]; in recent
decades, an increase in both the number of affected areas
and the number of detected cases in such areas has been
noted, corresponding to declining population immunity
after the eradication of smallpox and thus the cessationof smallpox vaccination. Against this background, recent
mathematical modelling studies revealed clear evidenceof the potential for further mpox outbreaks [8].
This epidemic potential was realised in 2022, which saw
outbreaks in several countries where mpox was previously non-endemic. These outbreaks were distinct in thatthe disease predominantly spread in and affected men
who have sex with men (MSM) [9–11]. Modelling studies have since shown that a heavy-tailed distribution ofsexual contacts, with a subgroup of the MSM population
having many more sexual partners than the mean (sometimes called the ‘core group’), could sustain an mpox
outbreak based on sexually associated contact transmission alone [12]. More recently, there has also been evidence of potential sexual contact transmission during the2023 outbreak in the Democratic Republic of Congo [13].
However, previous evidence [14] and a few confirmed
cases in children during the recent outbreaks [15] suggestthat the virus is not transmitted solely through contacts
associated with sexual activity, and more general forms ofclose or physical contact can also be means of human-tohuman transmission. Theoretically, then, the virus should
also find it easy to spread in other settings with a large
number of physical contacts, like care homes and kindergartens, daycare centres, or other such childcare andeducation institutions.
That the majority of detected infections during therecent outbreaks have been in the MSM community andbarely any have been in children, care home residents
and such [9–11] could imply that the probability of transmission during sexually associated physical contacts ismuch higher than that during other forms of physicalcontact. However, epidemiological studies quantifying
these parameters are scarce, given the private and sometimes anonymous nature of sexual contacts, especiallyin the core group [16], as well as the lack of substantial

Page 2 of 11

transmission in other settings. Uncertainty also surrounds the quantification of the immunity to mpox conferred by the smallpox vaccine in different age groups
dependent on time since vaccination, and the proportionof the population that has had the smallpox vaccinationin the first place, although in theory ascertaining theseparameters should be an easier task.
Faced with these uncertainties, efforts to model the
recent outbreak and proposed or implemented interventions have been limited by the need to make many
assumptions about key parameters or consider a very
wide range of scenarios [12, 17–19]. In this paper, we
present a compartmental infection dynamics modelthat can simulate transmission in different contact networks/settings and also model contact tracing that cantake into account realistic delays and contact patterns,
without the added computational and conceptual complexities of a network model or an agent-based model.
We use this model to determine which epidemiologicaland behavioural parameters the transmission of mpox ismost sensitive to, with a focus on infections in the MSM
community and other high physical-contact contexts likekindergartens and care homes. We believe that this information can be used to help guide the prioritisation of
resources in epidemiological studies to the most impactful parameters and can also help infectious disease modelling efforts ascertain which parameters can be safely
fixed at assumed values and which parameters call for
more scrutiny. We also investigate the efficacy of population-level interventions at controlling the spread of mpox
and how sensitive this efficacy is to various efficiency or
accuracy parameters related to the intervention. Thiscan help guide improvements in certain aspects of nonpharmaceutical interventions and is thus useful for future
outbreak preparedness.

Methods
Model

Our model is a compartmental, discrete-time, stochastic model that describes the epidemiological dynamics
of mpox infection in an S-E-I-R (Susceptible-ExposedInfectious-Recovered) framework, with additional
compartments to model quarantine and isolation of individuals, and the presence of asymptomatic or otherwise
undetectable infection. In the main text, we present only
the main features of the model; a complete and formal
definition is supplied in Supplementary File 1 [20–38].
The model was built using the odin.dust package (version
0.3.9) [39] in R 4.3.1 [40]. We used evidence from previous studies to inform the model structure when possible. However, given the recency of the outbreaks and thecomplexity of our model especially with regard to themetapopulation structure, it was not always possible toChaturvedi et al. BMC Medicine(2024) 22:297

find relevant studies to base model structure on, and wemade educated assumptions in these cases.
Metapopulations

The population in the simulation is stratified into 12 agegroups (0–4, 5–9, 10–14, 15–17, 18–24, 25–34, 35–44,
45–54, 55–64, 65–69, 70–74, 75 +). A proportion of theyoungest age group (0–4 years old) is assumed to attend
a kindergarten, daycare, or other such institution, anda proportion of the population above the age of 65 isassumed to consist of care home residents. Some individuals in the age groups that comprise the 18–65 band
are assumed to be teaching staff in kindergartens/daycares, and some are carers in care homes. Furthermore, aproportion of the 18–74-year-olds (in each setting except
care home residents) are men who have sex with men(MSM), and the MSM subpopulation is further divided
into high and low sexual activity groups.
We have made efforts to ensure that the distributionof the population into these metapopulations is similar
to the real distribution thereof in the population of Berlin, Germany. However, the numbers are estimates fromvarious data sources (described in Supplementary File 1)
and some inconsistencies needed to be resolved based onassumptions.
Transmission routes and course of infection

We assumed that the mpox virus can be transmitted
through any sort of close, physical contact, but has amuch higher probability of transmission through contacts which include a sexual component. Therefore, themodel allows for four routes of transmission: throughsexual contacts; household contacts; contacts between
children and teachers and children and children in kindergarten settings; and contacts between residents andcarers and residents and residents in care home settings.
The pre-infectious period of the virus is assumed tobe the same as the incubation period, variable, and follow a log-normal distribution based on previous evidence[22]. Variability in the pre-infectious period is modelledby having sub-compartments of the exposed compartment that track the number of days since the start of the
incubation period and then assigning probabilities oftransitioning to the infectious stage for each day of the
pre-infectious period.
The infectious period is also assumed to be variable
and is modelled using a gamma distribution as a more
realistic alternative to the often implicitly used exponential distribution [41], with transitions to the Recovered compartment modelled similar to transitions fromthe Exposed to Infectious compartments. The Infectious
compartment is split up into ‘Detectable’ and ‘Undetectable’ compartments. Undetectable infectious individuals

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go through the infectious period and recover and cantransmit infection to others throughout the infectious
period. Detectable infectious individuals have a probability of being detected on each day of the infectious period
bar the first two, although they may recover without everbeing detected. On detection, these individuals isolate
and do not have further contact (in the sense of physicalcontact) or infect anyone else.
Existing immunity

We assumed an all-or-nothing model for the immunity to mpox conferred by the smallpox vaccination, i.e.
we assumed that a proportion of individuals who have
had the smallpox vaccination in the past are completely
immune (in which case we move them to the Recovered
compartment at the start of simulation), and the rest are
equally as susceptible to mpox as those without smallpox
vaccinations. The proportion of people who have such
immunity depends on both the proportion of people ineach age group who were vaccinated and the level of protection provided by a smallpox vaccination.
We expect that the proportion of people who were
vaccinated against smallpox would be higher in theolder age groups than the younger age groups, as smallpox vaccination was slowly phased out as the world got
closer to eradication. However, the vaccine may provide
more immunity in the younger age groups, if the immunity provided this way wanes quickly. Therefore, theproportion of individuals in the entire population thathave immunity to mpox due to a smallpox vaccination ispotentially a complex, two-parameter function of age. In
the analyses, we assumed that immunity conferred thisway does not wane and that the proportion of individuals
vaccinated against smallpox decreases linearly from 90%
in the oldest age group to 40% in the youngest age groupold enough to have been alive during smallpox vaccination drives in Germany (the 35–45 years old group). The
model parameter governing immunity can then be interpreted as the level of immunity to mpox conferred by thesmallpox vaccination.
Non‑pharmaceutical interventions

The non-pharmaceutical interventions (NPIs) employedin Germany to combat the 2022 mpox outbreaks were a
combination of contact tracing, targeted pre-exposure
vaccinations for those deemed to be at high risk, andpost-exposure vaccinations of traced contacts (ring vaccinations). We consider the same NPIs in our model.
In the model, susceptible and exposed individuals aretraced with a probability dependent on when they werelast contacted by an infectious, detectable individual, anda base tracing probability that represents parameters liketracing accuracy, adherence to tracing regulations, etc.

Chaturvedi et al. BMC Medicine(2024) 22:297

There is also a lag in tracing, assuming that there will bea delay between a case being detected and their contacts
being traced. Furthermore, all traced contacts are vaccinated if ring vaccinations are active, but the proportion
successfully immunised is governed by a ‘vaccination
efficacy’ parameter, not to be confused with the smallpox
vaccination parameter that determines how many individuals had pre-existing immunity due to the smallpox
vaccination.
To model pre-exposure vaccinations, we assume thata number of vaccinations are offered to the ‘high risk’group (defined in this instance by the Robert Koch Institute as individuals in the MSM community that have ahigh frequency of sexual contacts [42], mirrored in themodel as the high sexual activity subgroup of the MSM
metapopulation) every day, and successful immunisationis governed by the same ‘vaccination efficacy’ parameteras in ring vaccinations.
In line with the Robert Koch Institute guidelines [20],we assume that this vaccination can also successfully
immunise exposed individuals who are in the first 4 daysof their incubation period.
Calibration

We fit the model to data about reported cases of mpox
per calendar week (for calendar weeks 21–45) in Berlin,
obtained from the Robert Koch institute database SurvStat [43]. We initialised our model at the start of calendar
week 19 and assumed that the observed data would be
Poisson-distributed around the cases detected in a week
in the model (with a small amount of noise added to
avoid zero expectation). We used the R package mcstateversion 0.9.18 [44] to run a particle Markov chain Monte
Carlo (pMCMC) algorithm and took means of the samples generated as the fitted parameter values. Comprehensive details about the pMCMC run are given in
Supplementary File 2 [43–45]. Table 1 shows the parameters included in the fitting process, along with bounds

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on their values. During the 2022 outbreaks, the smallpox
vaccine IMVANEX—previously used in smallpox immunisation drives—was used for pre- and post-exposure
vaccinations against mpox in Germany [20]. Therefore,
for calibration, the same parameter governs both immunity due to previous smallpox vaccination and immunity
conferred by vaccination administered as part of nonpharmaceutical interventions.
We assumed a lag in tracing of 2 days and an average of
200 daily pre-exposure vaccinations offered.
Analyses

We used the global sensitivity analysis method developedby Sobol [46] to estimate the magnitude of the impactthat variance in input parameters has on various model
outputs.
Sets of input parameters were sampled from definedbounds using Saltelli’s scheme [47] and for each set theoutputs were calculated as the means of 15 runs of thestochastic model. Parameter sampling and subsequent
analysis was done using the Python library SALib version
1.4.7 [48], using the R package reticulate version 1.34.0[49] to interface with R in order to run the model. We
used total order Sobol indices as a measure of model sensitivity. These indices indicate what amount of variancein a designated model output is caused by variance in thevarious parameters in the analysis, taking into accountinteractions between the parameters [50].
We conducted four analyses—two concerning epidemiological and behavioural parameters and twoconcerning parameters associated with public healthinterventions. All parameters not included in a particular analysis were fixed at their calibrated values
unless explicitly mentioned otherwise. This means thatthe analyses about epidemiological parameters involve
transmission dynamics under contact tracing and preexposure vaccinations, and the analyses about intervention parameters assume transmission dynamics

Table 1 Parameters that were calibrated using case data from Berlin, and the bounds within which they were calibrated
Parameter to be fitted

Bounds

Probability of transmission per non-sexual contact(0.0, 0.1)

Probability of transmission per sexual contact(0.0, 0.5)

Proportion of infections that are detectable(0.5, 1.0)

Initial number of infections (per age group in which infections initialised) (integer)(0, ∞)

Ratio of sexual contacts of core MSM group to rest of MSM population(10.0, 30.0)

Assortativity in sexual mixing between core group and rest of MSM population(0.5, 1.0)

Probability that vaccination confers immunity*(0.5, 1.0)

Base probability that a contact of a detected case will be traced(0.5, 1.0)*

The same vaccination parameter governs immunity due to a previous smallpox vaccination and immunity due to pre- and post-exposure vaccinations as part ofnon-pharmaceutical interventions

Chaturvedi et al. BMC Medicine(2024) 22:297

similar to the 2022 outbreaks. Unlike during the calibration process, here, we distinguished between thevaccination efficacy of the smallpox vaccination andthe efficacy of the vaccine used for pre- and post-exposure vaccinations during the outbreak. This was done
to make the analysis generalisable to situations wherea different vaccine than the smallpox vaccine may be
used as part of non-pharmaceutical interventions.
For all four analyses, we investigated the impact of
the included parameters on the cumulative number of
infections after 50, 100, and 365 days in, kindergartengoing children, care home residents, and the MSM
subpopulation.
Analysis 1.1: Epidemiological and behavioural parameters,
transmission similar to 2022 outbreaks

The first analysis contained three epidemiological andbehavioural parameters that we identified as potentiallyhighly impactful on mpox transmission dynamics during the 2022 outbreaks and for which there exist gaps inempirical knowledge. These are shown in Table 2, alongwith the ranges explored in the sensitivity analysis.
Analysis 1.2: Epidemiological and behavioural parameters,
wider transmission

For this analysis, we included all the parameters fromanalysis 1.1, and also included the probability of transmission per non-sexual contact as a varying parameter (varied from 0.0 to 0.1), since theoretically mpox
transmission is not limited to just sexual contacts.
Analysis 2.1: Intervention parameters, contact tracing, pre‑and post‑exposure vaccinations

In the first of two global sensitivity analyses about
the impact of intervention parameters, we included
two vaccination parameters—number of daily preexposure vaccinations offered and efficacy of the vaccine—and two tracing parameters, namely the baseprobability that a contact would be traced and thedelay between a case being detected and their contacts
being traced. The ranges explored for each of theseparameters are given in Table 3.

Page 5 of 11

Table 3 Parameters included in sensitivity analysis 2.1, alongwith the ranges within which they were variedParameter

Range

Mean number of daily pre-exposure vaccinations (integer)[50, 250]

Probability of vaccine conferring immunity[0.5, 1.0]

Base probability that a contact of a detected case will be
traced[0.1, 1.0]

Delay between case being detected and their contacts being
traced (days) (integer)[0, 10]Analysis 2.2: Intervention parameters, contact tracing
and post‑exposure vaccinations

To investigate important intervention parameters in scenarios with low vaccine availability, we set the number of
pre-exposure vaccinations to zero and ran a sensitivity
analysis consisting of the tracing parameters included inanalysis 2.1 and efficacy of (post-exposure) vaccinations.

Results
Calibration

The results of the model calibration process, including
fitted parameter values, post-fitting checks, and traceplots for the pMCMC, are given in Supplementary File 2.
Analysis of epidemiological and behavioural parameters
Analysis 1.1

We found that in our analysis of scenarios similar to the2022 outbreaks (i.e. a very low transmission probability
on non-sexual contact, contact tracing in place, and preand post-exposure vaccinations offered), variance in all
included parameters contributed moderately to greatly tovariance in the model outputs, as indicated by the totalorder Sobol indices in Table 4. The transmission probability per sexual contact was the dominant contributor
to model dynamics throughout, with Sobol indices ranging from 0.61 to 0.76 across all outputs considered. Variance in the probability of a previous smallpox vaccination
granting immunity contributed moderately to variancein the outputs and increased slightly over time (indicated by the Sobol indices for cumulative infections after
50 days being smaller than the Sobol indices for cumulative infections after 100 or 365 days). Variance in theratio of sexual contacts of the core group to the non-core

Table 2 Parameters included in sensitivity analysis 1.1, along with the ranges within which they were variedParameter

Range

Probability of transmission per sexual contact[0.2, 0.7]

Ratio of sexual contacts of core MSM group to rest of MSM population[10, 30]

Probability that previous smallpox vaccination confers immunity[0.3, 1]Chaturvedi et al. BMC Medicine(2024) 22:297

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Table 4 Total order Sobol indices for the sensitivity analyses regarding analyses 1.1 and 1.2. The outputs considered are cumulative
infections after 50, 100, and 365 days of simulation in the MSM community (MSM), kindergarten-going children (KG), and care homeresidents (Care)
Total order Sobol indices for cumulative infection after:

50 daysMSM

100 days
KG

Care

MSM

365 days
KG

Care

MSM

KG

Care

Analysis 1.1. Epidemiological and behavioural parameters, transmission similar to 2022 outbreaks
Probability of transmission on sexual contact

0.62

0.68

0.64

0.61

0.66

0.57

0.61

0.62

0.25

Probability of immunity given smallpox vaccination

0.28

0.15

0.32

0.33

0.27

0.47

0.33

0.42

0.76

Ratio of sexual contacts of core group to non-core group

0.38

0.40

0.38

0.27

0.30

0.27

0.25

0.10

0.09

Analysis 1.2. Epidemiological and behavioural parameters, wider transmission*

Probability of transmission on non-sexual contact

0.00*

0.68

0.73

0.01

0.81

0.84

0.62

0.99

0.94

Probability of transmission on sexual contact

0.61

0.39

0.31

0.60

0.33

0.12

0.22

0.00*

0.00*

Probability of immunity given smallpox vaccination

0.28

0.08

0.23

0.33

0.13

0.20

0.20

0.00*

0.08

Ratio of sexual contacts of core group to non-core group

0.40

0.19

0.19

0.26

0.13

0.05

0.04

0.00*

0.00*

< 0.005, rounded to 0.00

MSM group also contributed moderately to variance inthe considered outputs, but this contribution decreased
over time.
Analysis 1.2

When the transmission probability per non-sexual contact was also varied in the sensitivity analysis, we foundthat it was the dominant contributor to variance in allmodel outcomes except cumulative infection after 50
and 100 days in the MSM subpopulation. Variance in thetransmission probability per sexual contact contributed
moderately to variance in infections in the MSM subpopulation throughout and to a lesser extent cumulative

infections after 50 and 100 days in care home residents
and kindergarten-going children. However, it had close
to no contribution to long-term dynamics—as indicatedby cumulative infections after 365 days—in care homeresidents and kindergarten-going children. Figure 1 provides a visual demonstration of the differing sensitivityof cumulative infections after 365 days in kindergartengoing children to variance in the probabilities of transmission per non-sexual and sexual contact respectively.
The implication that, in this scenario, long-term mpox
dynamics are mostly driven by non-sexual contacts isfurther strengthened by the Sobol indices for the ratio of
sexual contacts of the core group to the no-core group;

Fig. 1 Cumulative infections in kindergarten-going children plotted against transmission probabilities. The clear vertical trend in the plot
against transmission per non-sexual contact (left) indicates that cumulative infections in kindergarten-going children are very sensitive to thisparameter, whereas the horizontal strata in the plot against transmission per sexual contact (right) on the right show that variance in this parameter
is not a major contributor to variance in the number of cumulative infections in kindergarten-going children

Chaturvedi et al. BMC Medicine(2024) 22:297

Page 7 of 11

cumulative infections after 50 and 100 days in all threeconsidered subpopulations are somewhat sensitive tothis ratio, but it contributes very little to variance in thenumber of cumulative infections after 365 days in any
considered subpopulation. Finally, infection numbers in
the MSM subpopulation and care home residents were
somewhat sensitive to the probability of immunity via
previous smallpox vaccination, whereas infection numbers in kindergarten-going children were less sensitive tothis parameter.
All Sobol indices from this analysis are displayed inTable 4.
Analysis of intervention parameters

Since the sensitivity analyses of intervention parameters
were conducted with epidemiological parameters reflecting the 2022 outbreaks, the probability of transmission
per non-sexual contact was very low. This meant that the
number of (cumulative) infections in kindergarten-goingchildren and care home residents was small, especiallyafter only 50 days of simulation. This makes interpretation of the Sobol indices for these outcomes difficult,and we do not discuss them below but have chosen to
include them in the results table (Table 5) for the sake ofcompleteness.
Analysis 2.1

We found that, when pre-exposure vaccinations were
implemented in addition to contact tracing and postexposure vaccinations, variance in the parameters
governing vaccination, i.e. the mean daily number of
pre-exposure vaccinations offered and the efficacy ofthe vaccine, contributed greatly to variance in cumulative infections in the MSM community (as shown by the

Sobol indices in Table 5). This dwarfed the contributionof variance in the tracing delay and base tracing probability. In contrast, variance in the tracing parameters contributed more than variance in vaccination parameters tocumulative infection variance in kindergarten-going children and care home residents, especially in cumulative
infection after 365 days.
Analysis 2.2

When pre-exposure vaccinations were not in place, we
found that all considered model outputs were very sensitive to both the delay in contact tracing and the baseprobability that a contact would be traced. This can beseen in the Sobol indices in Table 5 and the scatter plots
in Fig. 2. Variance in the efficacy of (post-exposure) vaccinations contributed far less to output variance thaneither tracing parameter.

Discussion
The model we have presented here allows for the simulation of an epidemic of mpox or a similar disease indifferent high-contact settings and for the realistic implementation and analysis of non-pharmaceutical interventions to contain the epidemic. The model is tailored not
towards prediction modelling or exact forecasts, but
towards comparing scenarios and non-pharmaceuticalinterventions, and identifying parameters that have alarge impact on the course of an mpox outbreak.
Estimates of the secondary attack rate—an approximation for the per-contact transmission probability—fromprevious outbreaks [14] do not distinguish between
sexual and non-sexual contacts. Our findings showedthat the infection dynamics of mpox are very sensitive
to the transmission probability per non-sexual contact.

Table 5 Total order Sobol indices for the sensitivity analyses regarding analyses 2.1 and 2.2. The outputs considered are cumulative
infections after 50, 100, and 365 days of simulation in the MSM community (MSM), kindergarten-going children (KG), and care homeresidents (Care)
Total order Sobol indices for cumulative
infection after:

50 daysMSM

100 days
KGa

Carea

MSM

365 days
KG

Care

MSM

KG

Care

Analysis 2.1. Intervention parameters, contact tracing, pre- and post-exposure vaccinations
Delay in tracing

0.04

0.21

0.32

0.02

0.08

0.11

0.02

0.24

0.72

Base probability of being traced

0.02

0.17

0.39

0.02

0.08

0.13

0.03

0.49

0.24

Probability of vaccine immunising

0.18

0.27

0.38

0.29

0.20

0.18

0.34

0.15

0.06

Daily (mean) pre-exposure vaccinations

0.78

0.72

0.70

0.67

0.68

0.69

0.63

0.18

0.01

Analysis 2.2. Intervention parameters, contact tracing and post-exposure vaccinationsaDelay in tracing

0.74

0.76

0.80

0.67

0.58

0.61

0.65

0.34

0.24

Base probability of being traced

0.42

0.53

0.68

0.41

0.50

0.48

0.42

0.66

0.75

Probability of vaccine immunising

0.04

0.28

0.42

0.02

0.01

0.02

0.03

0.01

0.03

There was very little variance in absolute terms in these outputs, due to low non-sexual transmission. Sobol indices for these terms should thus be interpreted withcautionChaturvedi et al. BMC Medicine(2024) 22:297

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Fig. 2 Cumulative infections in the MSM community plotted against contact tracing parameters. The plot shows cumulative infections in the MSM
community plotted against (left) delay in tracing with colour indicating base probability of being traced and (right) base probability of being
traced with colour indicating delay in tracing in analysis 2.2. The clear vertical trends indicate the sensitivity of the infection dynamics in the MSM
community to both tracing parameters of cumulative infections in the MSM community to both these parameters in analysis 2.2

Variance in the transmission probability per sexual contact contributed somewhat to variance in the short-term
dynamics, but in the long run, its effect was dwarfed bythat of transmission through non-sexual contacts, indicating that in these scenarios the epidemic was triggered by sexual contacts but sustained by non-sexual
contacts. This could simply be due to the fact that the
majority of physical contacts are not sexual. However, if
the transmission probability per non-sexual contact wasvery low, as we believe it to be—and as the calibration
results suggest—in the outbreaks of 2022, the course of
the epidemic was very sensitive to the transmission probability per sexual contact throughout, and the epidemic
could only be sustained by sexual contacts. Therefore, aprecise understanding and quantification of both theseparameters separately is necessary to support modelling
efforts for future outbreaks. However, precise estimation of transmission probabilities is always challenging,and estimation of the transmission probability per sexual
contact in particular is often hindered by the intimate—and sometimes anonymous—nature of sexual contacts.
The same is true for trying to quantify the higher levelof sexual activity of the core group, which is the othersexual-associated parameter we investigated and found
dynamics to be sensitive to.
It is to be expected that the immunity provided by thesmallpox vaccine will have more of an impact on infection dynamics in the more elderly age groups, i.e., carehome residents and to some extent the MSM population
than the younger ones such as kindergarten-going children, and this is what we saw in our analyses. However,

we found that even under these assumptions the infection
dynamics in children and the MSM community—which
was skewed towards the younger age groups—were moderately sensitive to the level of such immunity. Despite
the limitations of our simplistic model and assumptionsof smallpox vaccinations and associated mpox immunity, it is clear that this immunity plays a crucial role inthe dynamics of an mpox outbreak. Therefore, attention
needs to be paid to how it is modelled in infectious disease models for mpox, and studies that can establish thelevel of pre-existing immunity to mpox in the population
due to the smallpox vaccination will be very useful toenable correct parametrisation of the same.
When non-pharmaceutical interventions consisted oftargeted pre-exposure vaccinations in addition to contact tracing and post-exposure vaccinations, we foundthat the number of pre-exposure vaccinations and vaccine efficacy contributed the most to variance in cumulative infections in the MSM community, but the tracing
parameters contributed more to variance in cumulative infections in kindergarten-going children and carehome residents. This is likely due to the facts that preexposure vaccinations were only administered in the
MSM ‘core group’ and infections were also initialised inthis group, spreading to kindergarten-going children andcare home residents only through secondary contacts.
This could imply that, in scenarios similar to the recent
outbreaks, effective contact tracing could help control
the spread of mpox, but improving vaccine efficacy anddistribution would help more towards entirely preventing
an epidemic. However, it should be noted that vaccine

Chaturvedi et al. BMC Medicine(2024) 22:297

development and procurement is challenging and expensive, and improvements may be more difficult to achieve.
Furthermore, in the absence of pre-exposure vaccinations, we found that transmission dynamics even in the
MSM community were sensitive to both the base probability of being traced, which can loosely be interpreted as
tracing accuracy and the lag between an infectious person being detected and their contacts being traced. We
also found that these parameters were interdependent,with accurate but slow tracing, as well as fast but inaccurate tracing not being very effective at reducing infection
numbers. Since tracing accuracy and tracing speed areantagonistic to an extent, our results suggest that a balance must be found between the two for effective contact
tracing.
We found variance in vaccine efficacy to have a relatively smaller effect on the infection dynamics when the
only way to administer vaccinations was through postexposure vaccination. This is likely due to the fact that
post-exposure vaccination is inherently dependent on
contact tracing, and therefore the effect of variance in the
tracing parameters dominates over the effect of vaccine
efficacy. This does not imply that post-exposure vaccination is not an effective control strategy. Indeed, there ismodelling-based evidence that it can be very effective at
containing smallpox outbreaks [51], and there is no reason to believe that this should be different with mpox.
One large limitation of this study is the contact matrix
framework we have used (and which is required by thecompartmental model approach). This implicitly assumes
some level of homogeneous population mixing, whichmight not be fully appropriate for the types of contacts
considered in the model. The same approach also makes
it difficult to model super-spreading events, and there isevidence that these played a large role in the recent outbreaks [52]. However, we have tried to mitigate this by
explicitly modelling a core group of individuals with anincreased frequency of sexual contacts, and the calibration and validation results in Supplementary File 2 indicate that our approach can successfully model mpox
dynamics in the general population. Furthermore, theparameters used to derive the contact matrices were
often based on generalisations of studies and literaturefrom different settings and countries, and the validity of
our contact matrices relies on the assumption that thesegeneralisations are valid. As an example for how this may
affect the study, a very low transmission probability is
not the only explanation for low observed incidence inchildren and non-MSM communities during the 2022
outbreaks; since the outbreak likely started in the MSM
community, it could simply be that the number of nonsexual physical contacts between the MSM community,
especially the core high activity group, and children andPage 9 of 11

other non-MSM communities is much lower than ourderived contact matrices imply. Another limitation isthat, although some reinfections have been reported [53],our model does not account for the possibility of reinfection with mpox. However, the number of reinfections issmall, and we do not believe that it has a large impact
on mpox outbreak dynamics. Neither does our modelaccount for other transmission routes such as from contaminated objects and injuries in health care settings, tattoo parlours, and the like, but similarly we do not believethat these routes contribute significantly to the overall
disease dynamics on a population level. Finally, we havegeneralised the sensitivity analysis of our model to mpox
models and dynamics in general. However, as with any
modelling-based study, it is possible that our results areartefacts of the specific model we chose and have limited
applicability otherwise.
Despite these limitations, we believe that our model
encapsulates the main features of mpox outbreak dynamics and associated non-pharmaceutical interventions andprovides a reasonable alternative to more complex agentbased and network models.

Conclusions
Our study suggests that further research and precise
quantification of parameters such as the SAR and thelevel of immunity to mpox provided by the smallpox vaccination, through region and population-specific epidemiological and behavioural studies, is necessary to enable
infectious disease modelling efforts—irrespective of thetype of model used—and be better prepared for future
outbreaks. Our study also suggests that improving vaccine efficacy and distribution of pre-exposure vaccinations would be an effective way of containing an mpox
outbreak and that the success of contact tracing andpost-exposure vaccinations depends on the speed andaccuracy of tracing equally.
Abbreviations
KG	Kindergarten-going children
MSM	Men who have sex with men

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s12916-​024-​03515-8.
Supplementary Material 1: Formal description of mathematical model,
Fig. S1.1, Tables S1.1–S1.4. Fig. S1.1: Model schematic. Table S1.1: Contact
and infection events in model. Table S1.2: Transition events in model.
Table S1.3: Events related to control strategies. Table S1.4: Sources for
demography parameters used.
Supplementary Material 2: Calibration and Validation of Model, Figs. S2.1–
S2.3, Tables S2.1–S2.4. Fig. S2.1: Trace and density plots for Markov Chain
Monte Carlo run. Fig. S2.2: Fitted model trajectories plotted against data
used for fit. Fig. S2.3: Fitted model trajectories plotted against data notused for fit. Table S2.1: Bounds on parameters to be calibrated. Table S2.2:

Chaturvedi et al. BMC Medicine(2024) 22:297

Initial values and proposal matrix variances for Markov Chain Monte Carlorun. Table S2.3: Labels for parameters used in figures. Table S2.4: Mean
post-calibration values of parameters as used in the model.
Acknowledgements
Not applicable
Authors’ contributions
MC, IR, BL, AK, and VKJ designed the study and constructed the model. MK
and SS were involved in model parametrisation and model construction in anadvisory role. MC conducted the analyses and visualisations. MC, VKJ, and AK
wrote the first draft of the manuscript. All authors read, edited, and approved
the final manuscript.
Authors’ X handles
Madhav Chaturvedi: @TheMadChatter1 from @ClinicalEpi.
Berit Lange: @kiina2001.
Mirjam Kretzschmar: @IDMUtrecht.
André Karch: @andkarch from @ClinicalEpi.
Veronika Jaeger: @eilewomisa from @ClinicalEpi.
Funding
Open Access funding enabled and organized by Projekt DEAL. This work was
supported by the Deutsche Forschungsgemeinschaft (German ResearchCouncil, project number 458526380), the Federal Ministry of Education andResearch (BMBF) via the Respinow project (Grant Number 031L0898F), theGerman Federal Ministry of Education and Research (BMBF) Network of
University Medicine 2.0: “NUM 2.0” via the project: Preparedness and Pandemic
Response in Germany – PREPARED (Grant Number 01KX2121) and theEuropean Union’s Horizon Europe research and innovation programme via the
SUNRISE project (Grant Agreement Number 101073821).
Availability of data and materials
All the code and data used for this manuscript are available at https://​zivgi​tlab.​
uni-​muens​ter.​de/​chatu​rve/​mpox.

Page 10 of 11

3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

13.
14.
15.

Declarations

16.

Ethics approval and consent to participate
Not applicable.

17.

Consent for publication
Not applicable.

18.

Competing interests
The authors declare that they have no competing interests.

19.

Author details
1
Institute of Epidemiology and Social Medicine, University of Münster, Münster, Germany. 2 Department of Epidemiology, Helmholtz Centre for Infection
Research, Brunswick, Germany. 3 Department of Epidemiology, University
Medical Center Utrecht, Utrecht, the Netherlands. 4 Martin-Luther-University
Halle-Wittenberg, Halle, Germany. 5 German Center for Infection Research,
Brunswick, Germany.

20.

21.
22.

Received: 15 February 2024 Accepted: 2 July 2024
23.

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